*Reduction completed without application of XY Wings,
Turbot fish, unique rectangles, guardians, etc; no
X wings or swordfish or forcing chains located.
(Sorry about the sloppy appearance of the grids;
I just don't seem to be able to line this stuff up)

First, if you want to get grids to line up nicely you need to use the "Code" and "/Code" tags in your post. Here's an example of what you need to write.

Code:

[code]
1 2 3 4 .
5 6 7 8 .
. . . . .
[/code]

Try reading the "FAQ" about this ... it gives a fairly good explanation.

As to the puzzle, I've already posted a pretty complete explanation in this forum, right here. Oh -- there's some other stuff in that post ... the discussion of this puzzle starts about half-way down. Here's the short version of how this puzzle can be resolved.

At the point you illustrated the grid of possibilities looks like this.

Keith, I also found an X Wing & XY Wing that helped me solve this puzzle; however I do not understand your "remote pair" concept. I "lightly" looked for an explanation online; but could not find any. My initial reaction is that I could not justify that this method is valid. Could you enlighten me as to when "remote pairs" can apply? Thanks in advance.

Remote pairs are not very common, but they are very easy to spot. If the puzzle has a number of squares that have the same two possibilities, see if you can chain these squares together.

Here is a pair

Code:

AB . . AB

No other square in the same row can have either the value A or the value B. Now suppose there are other squares which have the same possibilities. They might be laid out like this:

Code:

AB . . AB
. . . .
. . . .
. . . AB
. . . . .
. . . . AB

where the lower two are in the same block. Now, number the nodes in the chain. Each odd-numbered square is a pair with each even-numbered square. (Or, label them + and - as David does.) If a pair is not in the same Row, Column, or Block, they are a "remote pair".

In this case, the top left and lower right squares are a remote pair. The square labelled "*" below cannot be A or B.

Thanks guys. I'll have to print out your explanations & study them a bit. After those embarrassing, simple BUG puzzles I recently sent you, David, I decided to just work on getting better rather than bother you with additional puzzles.